PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Genetic decomposition of Integration
Page: 2-444
In this paper I present a theoretical analysis (genetic decomposition) in the sense of APOS theory, of the cognitive constructions for the concept of infinite Riemann sums and the Fundamental Theorems of Calculus as a linking tool between the derivative and the integral, following Piaget's model of epistemology. This genetic decomposition is primarily based on my own mathematical knowledge as well as on my personal continual observations of students in the process of studying integration. I also present empirical data in the form of informal interviews with students at different stages of learning. The analysis of those interviews will later suggest a review of the initial genetic decomposition. Based on this analysis I also suggest instructional procedures that motivate the mental activities described in the proposed genetic decomposition. This study will shed new lights on the concept and make the connections more obvious between two key concepts in calculus.